Find necessary and sufficient conditions an a,b,c,d so

Heather Dickson

Heather Dickson

Answered question

2022-04-12

Find necessary and sufficient conditions an a,b,c,d so that the equations
z2+az+b=0, z2+cz+d=0
are collinear in the plane.

Answer & Explanation

Assorrymarf0cgr

Assorrymarf0cgr

Beginner2022-04-13Added 10 answers

Step 1
They’re collinear iff
a24bc24d
and
a24b(ac)2
are positive reals.
a-c is twice the vector between the midpoints of both pairs. The determinants are the difference between the roots squared. Any complex number in the direction of a line, squared will give the same angle.

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